Minimizing security holdings risk during portfolio trading

ABSTRACT

A method and computer program product for minimizing short-term risk to a portfolio of securities holdings during implementation of executing an outstanding trade list of securities to be traded, takes into account covariances between securities in the outstanding trade list and between securities in the outstanding trade list and securities in the portfolio of holdings so as to minimize risk to the portfolio of holdings as well as to a residual trade list of unexecuted orders during said implementation.

FIELD OF THE INVENTION

This invention relates generally to trading strategies in securitiesmarkets. Particularly, the invention relates to a system and method forminimizing the overall risk to a portfolio of financial securityholdings during execution of a trade list of a large number ofsecurities.

BACKGROUND OF THE INVENTION

A securities trading mechanism can be thought of as a set of protocolsthat translate investors' latent demands into realized prices andquantities. Various automated trading systems are known, which executeso-called “program” trading strategies in response to market movements.

Traders for large institutional investors such as mutual funds, hedgefunds, etc. face a dilemma. On the one hand, they are responsible fortrading large blocks of stocks and cannot afford to send large marketorders that will result in adverse market impact and inferior executionprices. On the other hand, they require a certain degree of immediacy tobe able to complete their trades within a defined time horizon. It istherefore typical for such traders to utilize a trading strategy tocomplete execution of a trading list of a large number of differentsecurities within a specified or given time frame, wherein multiplesmaller orders for portions of the trading list are sent over the giventime frame according to a predefined trading strategy model thatminimizes the risk to the unexecuted portion of the trading list ofunfavorable market movements caused by execution of the smaller orders.

One such known trading risk objective strategy treats the unexecutedtrade list as a long-short portfolio and utilizes a multi-factor riskmodel to construct a minimal risk “portfolio” of unfilled orders to besent simultaneously for execution. The “portfolio” of unfilled orderswhen executed minimizes the risk to short-term return of the unexecutedtrade list.

The Markowitz Model (as described in “Portfolio Selection,” Dr. H. M.Markowitz, Journal of Finance, Mar. 7, 1952), is an optimization modelthat balances the expected return and risk of a portfolio to allow theconstruction of a minimal risk portfolio. The decision variables are theamounts invested in each asset. According to this model, the statisticalvariance a stock's price is used as a measure of its risk, the expectedreturn of the stock is used as a measure of its utility or long-termprospects, and the variance of a portfolio's return is derived from thecovariances for the returns of the individual assets in the portfolio.

Variance is a measure of the fluctuation in the rate of return, wherehigher variances indicate riskier investments, while covariance is ameasure of the correlation of return fluctuations of one asset (e.g.,stock) with the return fluctuations of another. A high covariancebetween two stocks indicates that an increase in one stock's return islikely to correspond to an increase in the other stock's return, a lowcovariance indicates that the return rates of the two stocks arerelatively independent, and a negative covariance indicates that anincrease in one stock's return is likely to correspond to a decrease inthe other stock's return. Thus, the risk of a portfolio is notdetermined by a simple weighted average of the risks of individualassets in the portfolio, but instead is determined by the mutualrelation between the returns of individual assets in the portfolio.

A shortcoming of the known trading risk objective model is that it failsto take into account the short-term effect that each trade has on theoverall portfolio of holdings, which includes securities held but nottraded as well as the unexecuted trade list of securities. Becauseportfolio managers are evaluated on the variance of their holdings'return, the actions of a trader using the known trading risk model mayhave an adverse effect on the short-term risk/return of the overallportfolio of holdings, since the trader is unaware of the portfolio'suntraded holdings. Here, it is assumed that there is little couplingbetween the long-term utility of the portfolio upon which the trade listis based, and the short-term utility that can be maximized using thetrade strategy.

There thus exists a need for improvements in the art to provide forcontrol of the short-term risk of the overall holdings of a portfolioupon which a trade list is based.

SUMMARY OF THE INVENTION

The present invention provides a method and computer program product forminimizing short-term risk to a portfolio of securities holdings duringimplementation of executing an outstanding trade list of securities tobe traded, including computer-executable instructions stored on acomputer-readable storage medium, including a computer program modulefor determining covariances between securities in the outstanding tradelist and between securities in the outstanding trade list and securitiesin the portfolio of holdings; a computer program module for receiving aquantity representing a portion of said trade list desired to beexecuted at a particular time; a computer program module for determininga residual trade list of securities not to be traded at said particulartime based on said covariances and said received quantity, which resultsin a minimum risk to said residual trade list and to said portfolio ofsecurities holdings; and a computer program module for determining anexecution trade list including identities and quantities of securitiesto be traded at said particular time by subtracting said residual tradelist from said outstanding trade list.

According to another aspect of the invention, a method is provided thatincludes the steps performed by the computer program product.

The present invention will become more fully understood from theforthcoming detailed description of preferred embodiments read inconjunction with the accompanying drawings. Both the detaileddescription and the drawings are given by way of illustration only, andare not limitative of the present invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram of a process for determining a minimal riskresidual trade list according to a preferred embodiment of the presentinvention; and

FIG. 2 is a block diagram of a system for implementing the process shownin FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As shown in FIG. 2, the trading risk model is implemented by a server201, which is in communication with various exchanges, such as anElectronic Communication Network (ECN) 205, the New York Stock Exchange206, the NASDAQ/OTC market 207, and other like markets/exchanges. Aclient 202 is composed of a PC, workstation or similar device, and maybe directed coupled to the server 201; other clients, such as client203, are coupled to the server 201 through a distributed communicationnetwork 204, which may be the Internet, a Wide Area Network (WAN), aLocal Area Network (LAN), or any other similar type of communicationnetwork.

Referring to FIG. 1, at step 101 a trader or other user inputs to theserver 201 the trade name (e.g., stock name or symbol), trading side(i.e., buy or sell) and quantity (e.g., dollar amount or number ofshares) for each component X_(ti) of a desired trade list X_(t). Here,buys may be denoted by a positive (+) sign and sells may be denoted by anegative (−) sign. At step 103, the trader or user inputs the tradename, side (i.e., long or short) and quantity of each component X_(Ii)of a portfolio of initial holdings X_(I). Again, long positions may bedenoted by a positive (+) sign and short positions may be denoted by anegative (−) sign.

At step 105, a covariance matrix R is constructed containing thecovariance R_(ij) for the components X_(tij) in the trade list, and thecovariance R_(ij) for the components in X_(t) against the components inX_(I). The covariance Rij between any two trade names can be determinedfrom historical trading data.

Next, at step 107 the quantity of shares (in terms of dollar amount orshare amount) desired to be traded in a current wave are inputted. Thisnumber may be determined in accordance with a specific trading strategyused by the trader (i.e., automated trade strategy or manuallyimplemented) taking into account various market data parameters. Suchtrading strategies are generally well known in the art and thus will notbe further discussed herein.

Once the quantity of shares to be executed in a current wave isinputted, at step 109 the components X_(ei) of an execution trade listX_(e) are determined that will minimize the risk to the resultingresidual trade list X_(r) as well as the static portion of the overallportfolio (which consists of the initial holdings X_(I), plus anyholdings X_(e) acquired in previous waves. Since the expected returnterms are linear and X_(t) is fixed, it is equivalent to determine thecomponents X_(ri) of the residual trade list X_(r).

The risk associated with the residual portfolio holdings may berepresented by the matrix term

X _(r) ^(T) RX _(r)

wherein all of the covariances among the residual securities are summed.Similarly, the risk associated with the residual-plus-static portfolioholdings may be represented by the matrix term

(X _(I) +X _(e) −X _(b))^(T) R(X _(I) +X _(e) −X _(b))

wherein X_(b) is a benchmark term (which may be zero).

Here, the notion of short term return α_(st) for each of the componentsof the residual trade list and the static holdings is defined as theexpected return over the time during which the trade list X_(t) isimplemented. For the purposes of the present invention, this notion ofshort-term return is separated from any long-term return prediction thatresulted in the choice of the trade list X_(t) in the first instance.Similarly, the notion of short-term risk λ_(st) for each of thecomponents is defined as an expected risk over the time that the tradelist is implemented.

An objective function may now be constructed of the form

c _(e)[α_(st)(X _(I) +X _(e))−λ_(st)((X _(I) +X _(e) −X _(b))^(T) R(X_(I) +X _(e) −X _(b)))]+c _(r)[α_(st) X _(r)−λ_(st) X _(I) ^(T) RX _(r)]

which takes into account the short-term interests of both the trader andthe portfolio manager. The constants c_(e) and c_(r) may be used to biasthe solution towards the overall holdings or the residual trade list.The objective function is solved for its maximum value so as todetermine a minimal risk residual trade list Xr (and thus an executionportion Xe) which also takes into account the short-term risk to theportfolio holdings.

At step 111, it is determined whether the entire trade list Xt has beencompleted. If so, the process ends at step 113; if not, the processreturns to step 107 to input the quantity desired for the next tradingwave.

As indicated in the above equations, the short-term risks and returnsare “taken into account” by including terms in the equationscorresponding to each of the risks/returns to be considered whencreating the minimal risk residual trade list or execution list.

Example

Suppose that a portfolio includes a short position of $2000 of IBM, andlong positions of $1000 of CSCO and $1000 of GM. A trade list X_(t) isto sell $1000 of GM, sell $1000 of CSCO, and buy $2000 of HPQ. Eachcomponent X_(ti) is the signed value of the ith stock we wish to trade.Thus, X_(t1)=1000, X_(t2)=1000, and X_(t3)=−2000 (where unfilled buysare negative and unfilled sells are positive. In other words, we are“short” our unfilled buys and “long” our unfilled sells). The covariancematrix R will reflect the fact that the covariance of CSCO and HPQ ishigh, the covariance of GM and HPQ and GM and CSCO are both low, and thecovariance of IBM and HPQ and IBM and CSCO are both high. In otherwords, CSCO, HPQ and IBM price movements have a positive correlation,while there is little or no correlation between the price movement of GMand any of IBM, CSCO and HPQ. The short position of IBM is representedas −2000. Mathematically, the covariance R₂₃ is large, while R₁₂ and R₁₃are small.

If we wish to complete half of the trade list in the current wave, theminimal risk residual portfolio Xr will consist of an outstanding sellorder for $1000 of CSCO and an outstanding buy order for $1000 of HPQ(since the minimum risk to the trade list given that one-half of thelist is to be implemented is to send the sell order for GM and half ofthe buy order for HPQ). Because the covariance IBM, CSCO and HPQ is alsohigh, the holdings risk is quite low since the short position IBMholding is not adversely affected by the residual (open) sell order forCSCO. However, if we had a $2000 long position of IBM in the static partof the portfolio, the holdings' risk would be quite high because theholdings portfolio would consist entirely of technology stocks as longpositions.

In this manner, the present invention simultaneously controls the riskof both the residual trade list and the overall holdings in theportfolio, and thus accounts for the interests of the portfolio manageras well as the trader.

The invention being thus described, it will be apparent to those skilledin the art that the same may be varied in many ways without departingfrom the spirit and scope of the invention. Any and all suchmodifications are intended to be included within the scope of thefollowing claims.

1. A method of minimizing short-term risk to a portfolio of securitiesholdings during implementation of executing an outstanding trade list ofsecurities to be traded, comprising the steps of: determiningcovariances between securities in the outstanding trade list and betweensecurities in the outstanding trade list and securities in the portfolioof holdings; receiving a quantity representing a portion of said tradelist desired to be executed at a particular time; determining a residualtrade list of securities not to be traded at said particular time basedon said covariances and said received quantity, which results in aminimum risk to said residual trade list and to said portfolio ofsecurities holdings; and determining an execution trade list includingidentities and quantities of securities to be traded at said particulartime by subtracting said residual trade list from said outstanding tradelist.
 2. The method of claim 1, wherein the step of determining saidresidual trade list takes into account a short-term return associatedwith said portfolio of holdings.
 3. The method of claim 1, wherein thestep of determining said residual trade list takes into account ashort-term return associated with said execution trade list.
 4. Themethod of claim 1, wherein the step of determining said residual tradelist takes into account a short-term risk associated with said portfolioof holdings.
 5. The method of claim 1, wherein the step of determiningsaid residual trade list takes into account a short-term risk associatedwith said execution trade list.
 6. A method of minimizing short-termrisk to a portfolio of securities holdings during implementation ofexecuting an outstanding trade list of securities to be traded,comprising the steps of: determining covariances between securities inthe outstanding trade list and between securities in the outstandingtrade list and securities in the portfolio of holdings; receiving aquantity representing a portion of said trade list desired to beexecuted at a particular time; determining an execution trade list ofsecurities to be traded at said particular time based on saidcovariances and said received quantity, which results in a maximumreturn to said execution trade list and to said portfolio of securitiesholdings; and determining a residual trade list including identities andquantities of securities not to be traded at said particular time bysubtracting said execution trade list from said outstanding trade list.7. The method of claim 6, wherein the step of determining said executiontrade list takes into account a short-term return associated with saidportfolio of holdings.
 8. The method of claim 6, wherein the step ofdetermining said execution trade list takes into account a short-termreturn associated with said execution trade list.
 9. The method of claim6, wherein the step of determining said execution trade list takes intoaccount a short-term risk associated with said portfolio of holdings.10. The method of claim 6, wherein the step of determining saidexecution trade list takes into account a short-term risk associatedwith said execution trade list.
 11. A computer program product forminimizing short-term risk to a portfolio of securities holdings duringimplementation of executing an outstanding trade list of securities tobe traded, comprising the following computer-executable instructionsstored on a computer-readable storage medium: a computer program modulefor determining covariances between securities in the outstanding tradelist and between securities in the outstanding trade list and securitiesin the portfolio of holdings; a computer program module for receiving aquantity representing a portion of said trade list desired to beexecuted at a particular time; a computer program module for determininga residual trade list of securities not to be traded at said particulartime based on said covariances and said received quantity, which resultsin a minimum risk to said residual trade list and to said portfolio ofsecurities holdings; and a computer program module for determining anexecution trade list including identities and quantities of securitiesto be traded at said particular time by subtracting said residual tradelist from said outstanding trade list.
 12. The computer program productof claim 11, wherein the program module for determining said residualtrade list takes into account a short-term return associated with saidportfolio of holdings.
 13. The computer program product of claim 11,wherein the program module for determining said residual trade listtakes into account a short-term return associated with said executiontrade list.
 14. The computer program product of claim 11, wherein theprogram module for determining said residual trade list takes intoaccount a short-term risk associated with said portfolio of holdings.15. The computer program product of claim 11, wherein the program modulefor determining said residual trade list takes into account a short-termrisk associated with said execution trade list.
 16. A computer programproduct for minimizing short-term risk to a portfolio of securitiesholdings during implementation of executing an outstanding trade list ofsecurities to be traded, comprising the following computer-executableinstructions stored on a computer-readable storage medium: a computerprogram module for determining covariances between securities in theoutstanding trade list and between securities in the outstanding tradelist and securities in the portfolio of holdings; a computer programmodule for receiving a quantity representing a portion of said tradelist desired to be executed at a particular time; a computer programmodule for determining an execution trade list of securities to betraded at said particular time based on said covariances and saidreceived quantity, which results in a maximum return to said executiontrade list and to said portfolio of securities holdings; and a computerprogram module for determining a residual trade list includingidentities and quantities of securities not to be traded at saidparticular time by subtracting said execution trade list from saidoutstanding trade list.
 17. The computer program product of claim 16,wherein the program module for determining said residual trade listtakes into account a short-term return associated with said portfolio ofholdings.
 18. The computer program product of claim 16, wherein theprogram module for determining said residual trade list takes intoaccount a short-term return associated with said execution trade list.19. The computer program product of claim 16, wherein the program modulefor determining said residual trade list takes into account a short-termrisk associated with said portfolio of holdings.
 20. The computerprogram product of claim 16, wherein the program module for determiningsaid residual trade list takes into account a short-term risk associatedwith said execution trade list.